What is (if there is) the generic term for equalities and inequalities I'm writing a text about a particular linear programming (LP)I optimization problem, that is described using a mixture of inequalities (≤, ≥) and equalities (=). My question now is: is there an generic term for these two concepts? Asking Google only yielded a message on sci.logic from 2012 without a helpful answer. Wikipedia surfing suggested "binary relation", but that is far too generic.
If the answer is "no" and there is a reason for that (e.g. because I am doing a mathematical fruit salad comparison), I would also accept that as an answer.
Edit clarifying why I am not simply relying on the fact that every LP can be transformed into canonical form ($\max\, \mathbf{c}^\textsf{T}\mathbf{x}\ \, s.t. \mathbf{Ax \leq b}, \mathbf{x \geq 0}$), und thus simply use the word inequality exclusively: in the text I am refering to a model written in a software environment similar to AMPL, which hides this transformation into canonical form and allows the user to use both equalities and inequalities in the problem definition.
 A: I know of no term to describe equalities and inequalities together without relying on some context.
In the context of linear programming, constraints probably captures both aspects nicely. But in more general optimization, other things could be considered constraints as well, like for example the constraint that a given variable must be an integer, which can't be expressed using (in)equalities.
In many branches of mathematics you can expect speakers to refer to them as relations or conditions if the context makes the meaning clear enough. That could either be because the speaker established the term up front, or because the audience has been staring at equalities and inequalities for several minutes so they know what they are talking about. In written texts, a clear definition is of course preferable. If you provide a local definition, you might as well define the term inequality itself to also include equalities. Some readers will get confused by this, but others will be grateful because the term is closer to their way of thinking.
The term “binary relations” would feel strange for both the spoken and the written use case, since it's too specific to be considered a simple abbreviation. It makes people think you're either talking about all binary relations, or you're for some reason emphasizing the fact that the relations are binary not ternary or whatever.
This answer includes input from several comments, so I'm making this community wiki.
